The invention is based on a vehicle brake system for reducing drive slip. An apparatus for reducing possible drive slip in the wheels has already been proposed, in German Pat. No. 18 06 671, for use in a vehicle having an internal combustion engine, a differential transmission and wheels which are driven by the differential transmission and with which wheel brakes are associated, and having at least one pressure reservoir as well as brake pressure control valves which have positions for buildup, maintenance and reduction of brake pressure. This apparatus includes means for measuring the angular velocities of the driven and the non-driven wheels; means for determining the magnitude of drive slip that occurs; and control switches which, if the magnitude of the drive slip exceeds a preselected upper switching threshold, moves the brake pressure control valve or valves of the slipping wheel or wheels into the positions for brake pressure buildup. If the slip value falls below this upper switching threshold, the brake pressure control valves are moved into their brake pressure maintenance position, and if the value falls below a second value, lower switching threshold, these valves are moved into the position for reducing brake pressure. This apparatus very quickly reduces drive slip to very low values. However, on road surfaces where the grip or traction varies, and especially while accelerating during startup using a friction clutch, this drastic reduction in drive slip can have the disadvantage that if the traction between the wheels and the road surface should increase suddenly, the vehicle engine will be braked down below its minimum rpm and will therefore stall. The engine will then have to be restarted and the vehicle started up and accelerated once again, yet the end result may be no different from before.